Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasi-bound states of the quantum dot.Comment: 23 pages, 16 figure

Spin transport theory in ferromagnet/semiconductor systems with non-collinear magnetization configurations

We present a comprehensive theory of spin transport in a non-degenerate semiconductor that is in contact with multiple ferromagnetic terminals. The spin dynamics in the semiconductor is studied during a perturbation of a general, non-collinear magnetization configuration and a method is shown to identify the various configurations from current signals. The conventional Landauer-B\"{u}ttiker description for spin transport across Schottky contacts is generalized by the use of a non-linearized I-V relation, and it is extended by taking into account non-coherent transport mechanisms. The theory is used to analyze a three terminal lateral structure where a significant difference in the spin accumulation profile is found when comparing the results of this model with the conventional model.Comment: 17 pages, 10 figure

Loop Quantum Cosmology IV: Discrete Time Evolution

Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a transformation from the connection to a dreibein representation and the selection of an internal time variable. Due to the discrete nature of geometrical quantities in loop quantum gravity also time turns out to be discrete leading to a difference rather than differential evolution equation. Furthermore, evolving observables are discussed in this framework which enables an investigation of physical spectra of geometrical quantities. In particular, the physical volume spectrum is proven to equal the discrete kinematical volume spectrum in loop quantum cosmology.Comment: 21 page

Structural and functional conservation of key domains in InsP3 and ryanodine receptors.

Inositol-1,4,5-trisphosphate receptors (InsP(3)Rs) and ryanodine receptors (RyRs) are tetrameric intracellular Ca(2+) channels. In each of these receptor families, the pore, which is formed by carboxy-terminal transmembrane domains, is regulated by signals that are detected by large cytosolic structures. InsP(3)R gating is initiated by InsP(3) binding to the InsP(3)-binding core (IBC, residues 224-604 of InsP(3)R1) and it requires the suppressor domain (SD, residues 1-223 of InsP(3)R1). Here we present structures of the amino-terminal region (NT, residues 1-604) of rat InsP(3)R1 with (3.6 Å) and without (3.0 Å) InsP(3) bound. The arrangement of the three NT domains, SD, IBC-β and IBC-α, identifies two discrete interfaces (α and β) between the IBC and SD. Similar interfaces occur between equivalent domains (A, B and C) in RyR1 (ref. 9). The orientations of the three domains when docked into a tetrameric structure of InsP(3)R and of the ABC domains docked into RyR are remarkably similar. The importance of the α-interface for activation of InsP(3)R and RyR is confirmed by mutagenesis and, for RyR, by disease-causing mutations. Binding of InsP(3) causes partial closure of the clam-like IBC, disrupting the β-interface and pulling the SD towards the IBC. This reorients an exposed SD loop ('hotspot' (HS) loop) that is essential for InsP(3)R activation. The loop is conserved in RyR and includes mutations that are associated with malignant hyperthermia and central core disease. The HS loop interacts with an adjacent NT, suggesting that activation re-arranges inter-subunit interactions. The A domain of RyR functionally replaced the SD in full-length InsP(3)R, and an InsP(3)R in which its C-terminal transmembrane region was replaced by that from RyR1 was gated by InsP(3) and blocked by ryanodine. Activation mechanisms are conserved between InsP(3)R and RyR. Allosteric modulation of two similar domain interfaces within an N-terminal subunit reorients the first domain (SD or A domain), allowing it, through interactions of the second domain of an adjacent subunit (IBC-β or B domain), to gate the pore

Consistency Conditions for Fundamentally Discrete Theories

The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to ensure that the numerical solutions can reliably be used as approximations to solutions of the differential equation. There are, however, also systems where a difference equation is deemed to be fundamental, mainly in the context of quantum gravity. Since difference equations in general are harder to solve analytically than differential equations, it can be helpful to introduce an approximating differential equation as a continuum approximation. In this paper implications of this change in view point are analyzed to derive the conditions that the difference equation should satisfy. The difference equation in such a situation cannot be chosen freely but must be derived from a fundamental theory. Thus, the conditions for a discrete formulation can be translated into conditions for acceptable quantizations. In the main example, loop quantum cosmology, we show that the conditions are restrictive and serve as a selection criterion among possible quantization choices.Comment: 33 page

First Penning-trap mass measurement in the millisecond half-life range: the exotic halo nucleus 11Li

In this letter, we report a new mass for $^{11}$Li using the trapping experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived nuclide, $t_{1/2} = 8.8 \rm{ms}$, for which a mass measurement has ever been performed with a Penning trap. Combined with our mass measurements of $^{8,9}$Li we derive a new two-neutron separation energy of 369.15(65) keV: a factor of seven more precise than the best previous value. This new value is a critical ingredient for the determination of the halo charge radius from isotope-shift measurements. We also report results from state-of-the-art atomic-physics calculations using the new mass and extract a new charge radius for $^{11}$Li. This result is a remarkable confluence of nuclear and atomic physics.Comment: Formatted for submission to PR

Isotropic Loop Quantum Cosmology

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the classical situation where space-time is inextendible. This effect is generic and does not depend on matter violating energy conditions, but it does depend on the factor ordering of the Hamiltonian constraint. Furthermore, it is shown that loop quantum cosmology reproduces standard quantum cosmology and hence (e.g., via WKB approximation) to classical behavior in the large volume regime where the discreteness of space is insignificant. Finally, an explicit solution to the Euclidean vacuum constraint is discussed which is the unique solution with semiclassical behavior representing quantum Euclidean space.Comment: 30 page

Interplay of chiral and helical states in a Quantum Spin Hall Insulator lateral junction

We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero in the central region and at moderate fields, we observe oscillations in resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.Comment: 5 pages, 4 figures, supp. ma

New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found